Pinning dynamic systems of networks with Markovian switching couplings and controller-node set

In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller-node set. Here, the coupling matrices and the controller-node sets change with time, induced by a continuous-time Markovian chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponentially stability of the coupled system. Two scenarios are considered here. First, we prove that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by the fixed pinning controller-node set, and in addition, the Markovian switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, in particular, for the problem of spatial pinning control of network with mobile agents, we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying system is stabilized. Two numerical examples are provided to demonstrate the validity of these theoretical results, including a switching dynamical system between several stable sub-systems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.Comment: 9 pages; 3 figure

Synchronization analysis of high order layered complex networks

In this letter, we propose high order layered complex networks. The synchronization is discussed in detail. The relations of synchronization, individual coupling matrices and the intrinsic function of the uncoupled system are given. As special cases, synchronization of monolayer networks and multiplex networks discussed in literature can be obtained

Cluster consensus in discrete-time networks of multi-agents with inter-cluster nonidentical inputs

In this paper, cluster consensus of multi-agent systems is studied via inter-cluster nonidentical inputs. Here, we consider general graph topologies, which might be time-varying. The cluster consensus is defined by two aspects: the intra-cluster synchronization, that the state differences between each pair of agents in the same cluster converge to zero, and inter-cluster separation, that the states of the agents in different clusters are separated. For intra-cluster synchronization, the concepts and theories of consensus including the spanning trees, scramblingness, infinite stochastic matrix product and Hajnal inequality, are extended. With them, it is proved that if the graph has cluster spanning trees and all vertices self-linked, then static linear system can realize intra-cluster synchronization. For the time-varying coupling cases, it is proved that if there exists T>0 such that the union graph across any T-length time interval has cluster spanning trees and all graphs has all vertices self-linked, then the time-varying linear system can also realize intra-cluster synchronization. Under the assumption of common inter-cluster influence, a sort of inter-cluster nonidentical inputs are utilized to realize inter-cluster separation, that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs. In addition, the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory. As an application, we employ a modified non-Bayesian social learning model to illustrate the effectiveness of our results.Comment: 13 pages, 4 figure

STUDIES ON THE FUNCT,IONS OF SPRINT EXERCISES ON JUVENIL'E JOINT TORQUE

The purpose of this study is to discuss the function of sprint on development of juvenile muscle strength. The study tests and the isokinetic strength of 30 ordinary healthy boys and girls and 30 ones from Physical Educational School, carrying out the test of the shoulder, hip and knee joints according to 3 different angular velocities: 600 /s, 1200 /s and 2400 /s. The main index of the test is: the Peak Torque of muscle tissues caused by joints extension and f1exion; poking into the function of sprint exercises on juvenile muscle's development. The outcome indicates that: sprint exercise has a distinctively positive effect on boys' development of the muscle strength of shoulders, hips and knees, and the coordination of the harmony of Flexion and Extension muscles. Whereas, sprint only exerts an apparently positive effect on girls' knees, but not hips and shoulders

Quantification and Purification of Mulberry Anthocyanins With Macroporous Resins

Total anthocyanins in different cultivars of mulberry were measured and a process for the industrial preparation of mulberry anthocyanins as a natural food colorant was studied. In 31 cultivars of mulberry, the total anthocyanins, calculated as cyanidin 3-glucoside, ranged from 147.68 to 2725.46 mg/L juice. Extracting and purifying with macroporous resins was found to be an efficient potential method for the industrial production of mulberry anthocyanins as a food colorant. Of six resins tested, X-5 demonstrated the best adsorbent capability for mulberry anthocyanins (91 mg/mL resin). The adsorption capacity of resins increased with the surface area and the pore radius. Residual mulberry fruit juice after extraction of pigment retained most of its nutrients, except for anthocyanins, and may provide a substrate for further processing

Asymmetrical Impact of Allee Effect on a Discrete-Time Predator-Prey System

A discrete-time predator-prey model is proposed with Leslie-type numerical response, and the asymmetrical influence of Allee effect on the proposed system is investigated. By mathematical analysis, locally stable conditions for the equilibrium points of the considered systems with or without Allee effect are obtained firstly. Furthermore, numerical simulation is used to verify the results and detect some new outcomes. The results show that Allee effect on predator leads the system to its stable state in much longer time. Conversely, the prey population with Allee effect makes it much faster. In particular, a large value of Allee effect on prey results in periodic dynamics of the system